A Program of The Actuarial Foundation. Aligned with Common Core State and NCTM Standards.
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What is an actuary? An actuary is an expert in statistics who works with businesses, governments, and organizations to help them plan for the future. Actuarial science is the discipline that applies math and statistical methods to assess risk.

Background photo: © Inga Nielsen/iStockphoto.

About This Lesson Plan



Bars, Lines, & Pies!

Bars, Lines, and Pies

Bar Graphs: A Statistical Skyline

Photo: © Stockbyte/Veer.
Photo: © Stockbyte/Veer.

In this lesson and activity, students understand how to use and read bar graphs.

Students will understand:

  • how to use bar graphs to represent, analyze, and generalize data patterns;
  • that bar graphs show trends in data and how one variable is affected as the other rises or falls;
  • how to propose and justify predictions based on bar graph analysis.

Reproducible Activity 2, sheet of graph paper, rulers, colored pencils, calculators


  1. Reproducible Activity 2: Bar Graphs
  2. Bonus Activity 2: Water Conservation: What Are the Winning Numbers?


  1. Distribute copies of Reproducible Activity 2. Read the “Raise the Bar” sidebar as a class. Explain to students that they will be learning about bar graphs in this activity. Tell students a bar graph is used to display and compare information. Explain that the height of each bar is proportional to the amount of data the bar represents. The higher the bar the larger the number or amount of data.
  2. Draw an X-axis (horizontal) and a Y-axis (vertical) on the board. Label each axis. On the X-axis write the different months of the year and on the Y-axis a sequence of numbers from 0 to 35 at intervals of 5. Use a show of hands to record the number of students born in each month of the year. Use this data to create an example of a bar graph. For example, 3 students were born in January, 7 in February, and so on.
  3. Explain that one axis of the graph is where the grouped data (months) is presented while the other is a frequency scale (number of students) showing the quantity of each group.
  4. When making a bar graph the data to be presented is used to create an appropriate interval scale. This scale helps people visualize and understand the data. (Point out the interval scale of the bar graph that you created.) Ask students how the graph would change in appearance if the scale were made of smaller intervals or larger intervals. A scale made of smaller intervals is better at illustrating small differences in bar height.
  5. Direct students to questions under “Work the Math.” Instruct them to create their first bar graph (Question 1) in the space provided and the second bar graph (Question 2) on a separate sheet of graph paper using the data provided in the table. Remind students to include a title and labels on their graphs and to neatly color in each bar. Once students have finished both graphs, instruct them to answer the remaining questions on the reproducible.
  6. When students are done, review the answers to the reproducible and invite them to share their bar graphs with the class.
  7. Have students explain differences in the data sets of bar graphs and pie charts. Ask how segment size and bar length perform similar functions in the two types of graphs.

Real-World Math:

  1. Ask students to think of graphs that they have seen in the real world. For what purposes were they used? Have students hunt for examples in books, in magazines, on the Internet, in newspapers, and in business documents.
  2. Review with students the definition of actuary on the poster. How can statistics help someone plan for the future? How might an actuary use graphs and math in the following real-world situations?

    --Help a school principal plan a recycling program. How could math and graphs show what the school has used in the past, and how much could be saved in the future by recycling? (Use past data to figure out future data [extrapolate], and compare results in a graph.)
    --Help the manager of a city plan for a second landfill. How much space would be needed for the new landfill? (Use past data from the first landfill, as well as data that reflects current use and extrapolate for future data. Display the findings in a graph.)
    --Help the manager of a company figure out how much money could be saved by recycling over a period of 10 years. (A line graph would reflect the increase of money saved over a period of time.)